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Class 9 Maths (NCERT)

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Module 1: Chapter 1: Number Systems

Introduction to Number Systems

ch1-introduction

Rational Numbers

ch1-rational-numbers

Exercise 1.1 - Detailed Solutions

ch1-exercise-1-1

Irrational Numbers

ch1-irrational-numbers

Exercise 1.2 - Detailed Solutions

ch1-exercise-1-2

Real Numbers & Decimal Expansions

ch1-real-decimals

Exercise 1.3 - Detailed Solutions

ch1-exercise-1-3

Operations on Real Numbers

ch1-operations

Rationalizing the Denominator

ch1-rationalization

Exercise 1.4 & 1.5 - Solutions

ch1-exercise-1-4-5

Laws of Exponents for Real Numbers

ch1-laws-exponents

Chapter 1 Summary

ch1-summary

Module 2: Chapter 2: Polynomials

What is a Polynomial?

ch2-introduction

Types of Polynomials

ch2-types

Zeroes of a Polynomial

ch2-zeroes

Exercise 2.1 - Detailed Solutions

ch2-exercise-2-1

Remainder Theorem

ch2-remainder-theorem

Factor Theorem

ch2-factor-theorem

Algebraic Identities

ch2-identities

Exercise 2.4 - Identity Applications

ch2-exercise-2-4

Chapter 2 Summary

ch2-summary

Module 3: Chapter 3: Coordinate Geometry

The Cartesian Plane

ch3-introduction

Understanding Coordinates

ch3-coordinates

Exercise 3.1 & 3.2 - Solutions

ch3-exercise-1-2

Exercise 3.3 - Plotting Points

ch3-exercise-3

Chapter 3 Summary

ch3-summary

Module 4: Chapter 4: Linear Equations in Two Variables

Linear Equations Introduction

ch4-introduction

Solutions of Linear Equations

ch4-solutions

Exercise 4.1 - Solutions

ch4-exercise-4-1

Exercise 4.2 - Solutions

ch4-exercise-4-2

Chapter 4 Summary

ch4-summary

Module 5: Chapter 5: Introduction to Euclid's Geometry

Euclid's Definitions & Axioms

ch5-definitions

Exercise 5.1 - Solutions

ch5-exercise

Module 6: Chapter 6: Lines and Angles

Types of Angles

ch6-types-angles

Parallel Lines & Transversal

ch6-parallel

Module 7: Chapter 7: Triangles

Congruence of Triangles

ch7-congruence

Properties of Triangles

ch7-properties

Module 8: Chapter 8: Quadrilaterals

Types of Quadrilaterals

ch8-types

Module 9: Chapter 9: Circles

Circle Properties

ch9-properties

Module 10: Chapter 10: Heron's Formula

Heron's Formula

ch10-herons-formula

Module 11: Chapter 11: Surface Areas and Volumes

Surface Areas

ch11-surface-areas

Volumes

ch11-volumes

Module 12: Chapter 12: Statistics

Data Presentation

data-presentation

Measures of Central Tendency

central-tendency

Module 13: Chapter 13: Constructions

Basic Constructions

basic-constructions

Triangle Constructions

triangle-constructions

Module 14: Chapter 14: Probability

Introduction to Probability

intro-probability

Experimental Probability

experimental-probability

Chapter 3: Coordinate Geometry

Exercise 3.3 - Plotting Points

Exercise 3.3 - Detailed Solutions

❓Question 1: Which quadrant?

Method:

Check signs of coordinates!

Coordinates	Signs	Quadrant
$(2, 3)$	$(+, +)$	I
$(-3, 2)$	$(-, +)$	II
$(-4, -3)$	$(-, -)$	III
$(3, -1)$	$(+, -)$	IV

❓Question 2: Plot and identify

$(x, y)$ where $x < 0$ and $y > 0$

$x < 0$ means x is negative $y > 0$ means y is positive

Signs: $(-, +)$ → Quadrant II

$(x, y)$ where $x > 0$ and $y < 0$

Signs: $(+, -)$ → Quadrant IV

❓Question 3: Rectangle from Points

Points: $A(-1, 3)$ , $B(-1, -4)$ , $C(5, -4)$ , $D(5, 3)$

Step 1: Plot the points

A is in Quadrant II
B is in Quadrant III
C is in Quadrant IV
D is in Quadrant I

Step 2: Join them in order

Step 3: Identify the shape The figure is a RECTANGLE ✓

Step 4: Find dimensions

Length (AB or CD): $|3 - (-4)| = 7$ units
Width (BC or AD): $|5 - (-1)| = 6$ units

Area = 7 × 6 = 42 square units

Visualizer

Coordinate Plane

Point A: (-1, 3)

Quadrant II

Interactive Visualization